Amazon.com: Google Apps: The Missing Manual 9780596515799: Nancy Conner: Books. This was a huge 500+ page book that was very wordy. She knew her stuff, but it was hard to be motivated to read it all. This would be worth reading for an administrator but I doubt the average person would read this tomb. I’m going to not suggest it simply because it is dated, and while mostly correct becomes less useful as time marches on.

I finally got a Senior Advisor, Taylor, at Apple to answer this. Three previous technicians claimed they’d never heard of this issue.
APACSD is Apple Wide Area Connectivity Service Daemon. It is a function of MobileMe. It doesn’t pertain to BTMM only, but to a world of connections such as Calendar, Contacts, Synch, iWeb, etc.
Taylor explained that this a a form of handshaking between MobileMe and your Mac. If the connection is disabled by your firewall protection, you will see many malfunctions in anything MobileMe-related.
hello.connectivity.me.com is a platform established in OSX 10.6.6 that will later support other added services.
Funny. The third technician thought I was worried about the government seeking contact with my computer (“just who do you believe is trying to access your computer?”) and treated me like a weirdo until I explained the research time I’d spent on this and told him I knew this was an Apple connection. Only then did he pass me along to his superior. At least he learned something.
And maybe this helps someone else who’s bugged by these repeated requests for access. Allow the connection and it’s over with.

MobileMe has had plenty of issues. Read about them here, here, here, here. I could go on, but I think you get the idea. I don’t know why I waited with MobileMe for 10 years. I guess I am slow to learn some things.